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Question

If y=y(x) is the solution of differential equation 2+sinxy+1(dydx)=cosx, y(0)=1, then y(π2) equals

A
73
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B
73
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C
13
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D
23
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Solution

The correct option is C 13
The given differential equation can be rewritten as:
1y+1dy=cosx2+sinxdx
Integrating both sides, we get
1y+1dy=cosx2+sinxdx
ln|y+1|+ln|c|+ln(2+sinx)=0
(Here, c is the constant of integration)
|c(y+1)|(2+sinx)=1(i)
when x=0, y=1
4c=±1c=±14
From (i)
|y+1|(2+sinx)=4
Now put x=π2
|y+1|3=4
y=13 or y=73

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